Polytope of Type {26,34}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,34}*1768
Also Known As : {26,34|2}. if this polytope has another name.
Group : SmallGroup(1768,49)
Rank : 3
Schlafli Type : {26,34}
Number of vertices, edges, etc : 26, 442, 34
Order of s0s1s2 : 442
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
13-fold quotients : {2,34}*136
17-fold quotients : {26,2}*104
26-fold quotients : {2,17}*68
34-fold quotients : {13,2}*52
221-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 18,205)( 19,206)( 20,207)( 21,208)( 22,209)( 23,210)( 24,211)( 25,212)
( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)( 32,219)( 33,220)
( 34,221)( 35,188)( 36,189)( 37,190)( 38,191)( 39,192)( 40,193)( 41,194)
( 42,195)( 43,196)( 44,197)( 45,198)( 46,199)( 47,200)( 48,201)( 49,202)
( 50,203)( 51,204)( 52,171)( 53,172)( 54,173)( 55,174)( 56,175)( 57,176)
( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,183)( 65,184)
( 66,185)( 67,186)( 68,187)( 69,154)( 70,155)( 71,156)( 72,157)( 73,158)
( 74,159)( 75,160)( 76,161)( 77,162)( 78,163)( 79,164)( 80,165)( 81,166)
( 82,167)( 83,168)( 84,169)( 85,170)( 86,137)( 87,138)( 88,139)( 89,140)
( 90,141)( 91,142)( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)
( 98,149)( 99,150)(100,151)(101,152)(102,153)(103,120)(104,121)(105,122)
(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,129)(113,130)
(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(239,426)(240,427)
(241,428)(242,429)(243,430)(244,431)(245,432)(246,433)(247,434)(248,435)
(249,436)(250,437)(251,438)(252,439)(253,440)(254,441)(255,442)(256,409)
(257,410)(258,411)(259,412)(260,413)(261,414)(262,415)(263,416)(264,417)
(265,418)(266,419)(267,420)(268,421)(269,422)(270,423)(271,424)(272,425)
(273,392)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)(280,399)
(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)(288,407)
(289,408)(290,375)(291,376)(292,377)(293,378)(294,379)(295,380)(296,381)
(297,382)(298,383)(299,384)(300,385)(301,386)(302,387)(303,388)(304,389)
(305,390)(306,391)(307,358)(308,359)(309,360)(310,361)(311,362)(312,363)
(313,364)(314,365)(315,366)(316,367)(317,368)(318,369)(319,370)(320,371)
(321,372)(322,373)(323,374)(324,341)(325,342)(326,343)(327,344)(328,345)
(329,346)(330,347)(331,348)(332,349)(333,350)(334,351)(335,352)(336,353)
(337,354)(338,355)(339,356)(340,357);;
s1 := ( 1, 18)( 2, 34)( 3, 33)( 4, 32)( 5, 31)( 6, 30)( 7, 29)( 8, 28)
( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)
( 17, 19)( 35,205)( 36,221)( 37,220)( 38,219)( 39,218)( 40,217)( 41,216)
( 42,215)( 43,214)( 44,213)( 45,212)( 46,211)( 47,210)( 48,209)( 49,208)
( 50,207)( 51,206)( 52,188)( 53,204)( 54,203)( 55,202)( 56,201)( 57,200)
( 58,199)( 59,198)( 60,197)( 61,196)( 62,195)( 63,194)( 64,193)( 65,192)
( 66,191)( 67,190)( 68,189)( 69,171)( 70,187)( 71,186)( 72,185)( 73,184)
( 74,183)( 75,182)( 76,181)( 77,180)( 78,179)( 79,178)( 80,177)( 81,176)
( 82,175)( 83,174)( 84,173)( 85,172)( 86,154)( 87,170)( 88,169)( 89,168)
( 90,167)( 91,166)( 92,165)( 93,164)( 94,163)( 95,162)( 96,161)( 97,160)
( 98,159)( 99,158)(100,157)(101,156)(102,155)(103,137)(104,153)(105,152)
(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145)(113,144)
(114,143)(115,142)(116,141)(117,140)(118,139)(119,138)(121,136)(122,135)
(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(222,239)(223,255)
(224,254)(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)
(232,246)(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(256,426)
(257,442)(258,441)(259,440)(260,439)(261,438)(262,437)(263,436)(264,435)
(265,434)(266,433)(267,432)(268,431)(269,430)(270,429)(271,428)(272,427)
(273,409)(274,425)(275,424)(276,423)(277,422)(278,421)(279,420)(280,419)
(281,418)(282,417)(283,416)(284,415)(285,414)(286,413)(287,412)(288,411)
(289,410)(290,392)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)
(297,402)(298,401)(299,400)(300,399)(301,398)(302,397)(303,396)(304,395)
(305,394)(306,393)(307,375)(308,391)(309,390)(310,389)(311,388)(312,387)
(313,386)(314,385)(315,384)(316,383)(317,382)(318,381)(319,380)(320,379)
(321,378)(322,377)(323,376)(324,358)(325,374)(326,373)(327,372)(328,371)
(329,370)(330,369)(331,368)(332,367)(333,366)(334,365)(335,364)(336,363)
(337,362)(338,361)(339,360)(340,359)(342,357)(343,356)(344,355)(345,354)
(346,353)(347,352)(348,351)(349,350);;
s2 := ( 1,223)( 2,222)( 3,238)( 4,237)( 5,236)( 6,235)( 7,234)( 8,233)
( 9,232)( 10,231)( 11,230)( 12,229)( 13,228)( 14,227)( 15,226)( 16,225)
( 17,224)( 18,240)( 19,239)( 20,255)( 21,254)( 22,253)( 23,252)( 24,251)
( 25,250)( 26,249)( 27,248)( 28,247)( 29,246)( 30,245)( 31,244)( 32,243)
( 33,242)( 34,241)( 35,257)( 36,256)( 37,272)( 38,271)( 39,270)( 40,269)
( 41,268)( 42,267)( 43,266)( 44,265)( 45,264)( 46,263)( 47,262)( 48,261)
( 49,260)( 50,259)( 51,258)( 52,274)( 53,273)( 54,289)( 55,288)( 56,287)
( 57,286)( 58,285)( 59,284)( 60,283)( 61,282)( 62,281)( 63,280)( 64,279)
( 65,278)( 66,277)( 67,276)( 68,275)( 69,291)( 70,290)( 71,306)( 72,305)
( 73,304)( 74,303)( 75,302)( 76,301)( 77,300)( 78,299)( 79,298)( 80,297)
( 81,296)( 82,295)( 83,294)( 84,293)( 85,292)( 86,308)( 87,307)( 88,323)
( 89,322)( 90,321)( 91,320)( 92,319)( 93,318)( 94,317)( 95,316)( 96,315)
( 97,314)( 98,313)( 99,312)(100,311)(101,310)(102,309)(103,325)(104,324)
(105,340)(106,339)(107,338)(108,337)(109,336)(110,335)(111,334)(112,333)
(113,332)(114,331)(115,330)(116,329)(117,328)(118,327)(119,326)(120,342)
(121,341)(122,357)(123,356)(124,355)(125,354)(126,353)(127,352)(128,351)
(129,350)(130,349)(131,348)(132,347)(133,346)(134,345)(135,344)(136,343)
(137,359)(138,358)(139,374)(140,373)(141,372)(142,371)(143,370)(144,369)
(145,368)(146,367)(147,366)(148,365)(149,364)(150,363)(151,362)(152,361)
(153,360)(154,376)(155,375)(156,391)(157,390)(158,389)(159,388)(160,387)
(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)(168,379)
(169,378)(170,377)(171,393)(172,392)(173,408)(174,407)(175,406)(176,405)
(177,404)(178,403)(179,402)(180,401)(181,400)(182,399)(183,398)(184,397)
(185,396)(186,395)(187,394)(188,410)(189,409)(190,425)(191,424)(192,423)
(193,422)(194,421)(195,420)(196,419)(197,418)(198,417)(199,416)(200,415)
(201,414)(202,413)(203,412)(204,411)(205,427)(206,426)(207,442)(208,441)
(209,440)(210,439)(211,438)(212,437)(213,436)(214,435)(215,434)(216,433)
(217,432)(218,431)(219,430)(220,429)(221,428);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(442)!( 18,205)( 19,206)( 20,207)( 21,208)( 22,209)( 23,210)( 24,211)
( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)( 32,219)
( 33,220)( 34,221)( 35,188)( 36,189)( 37,190)( 38,191)( 39,192)( 40,193)
( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,199)( 47,200)( 48,201)
( 49,202)( 50,203)( 51,204)( 52,171)( 53,172)( 54,173)( 55,174)( 56,175)
( 57,176)( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,183)
( 65,184)( 66,185)( 67,186)( 68,187)( 69,154)( 70,155)( 71,156)( 72,157)
( 73,158)( 74,159)( 75,160)( 76,161)( 77,162)( 78,163)( 79,164)( 80,165)
( 81,166)( 82,167)( 83,168)( 84,169)( 85,170)( 86,137)( 87,138)( 88,139)
( 89,140)( 90,141)( 91,142)( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)
( 97,148)( 98,149)( 99,150)(100,151)(101,152)(102,153)(103,120)(104,121)
(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,129)
(113,130)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(239,426)
(240,427)(241,428)(242,429)(243,430)(244,431)(245,432)(246,433)(247,434)
(248,435)(249,436)(250,437)(251,438)(252,439)(253,440)(254,441)(255,442)
(256,409)(257,410)(258,411)(259,412)(260,413)(261,414)(262,415)(263,416)
(264,417)(265,418)(266,419)(267,420)(268,421)(269,422)(270,423)(271,424)
(272,425)(273,392)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)
(280,399)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)
(288,407)(289,408)(290,375)(291,376)(292,377)(293,378)(294,379)(295,380)
(296,381)(297,382)(298,383)(299,384)(300,385)(301,386)(302,387)(303,388)
(304,389)(305,390)(306,391)(307,358)(308,359)(309,360)(310,361)(311,362)
(312,363)(313,364)(314,365)(315,366)(316,367)(317,368)(318,369)(319,370)
(320,371)(321,372)(322,373)(323,374)(324,341)(325,342)(326,343)(327,344)
(328,345)(329,346)(330,347)(331,348)(332,349)(333,350)(334,351)(335,352)
(336,353)(337,354)(338,355)(339,356)(340,357);
s1 := Sym(442)!( 1, 18)( 2, 34)( 3, 33)( 4, 32)( 5, 31)( 6, 30)( 7, 29)
( 8, 28)( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 35,205)( 36,221)( 37,220)( 38,219)( 39,218)( 40,217)
( 41,216)( 42,215)( 43,214)( 44,213)( 45,212)( 46,211)( 47,210)( 48,209)
( 49,208)( 50,207)( 51,206)( 52,188)( 53,204)( 54,203)( 55,202)( 56,201)
( 57,200)( 58,199)( 59,198)( 60,197)( 61,196)( 62,195)( 63,194)( 64,193)
( 65,192)( 66,191)( 67,190)( 68,189)( 69,171)( 70,187)( 71,186)( 72,185)
( 73,184)( 74,183)( 75,182)( 76,181)( 77,180)( 78,179)( 79,178)( 80,177)
( 81,176)( 82,175)( 83,174)( 84,173)( 85,172)( 86,154)( 87,170)( 88,169)
( 89,168)( 90,167)( 91,166)( 92,165)( 93,164)( 94,163)( 95,162)( 96,161)
( 97,160)( 98,159)( 99,158)(100,157)(101,156)(102,155)(103,137)(104,153)
(105,152)(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145)
(113,144)(114,143)(115,142)(116,141)(117,140)(118,139)(119,138)(121,136)
(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(222,239)
(223,255)(224,254)(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)
(231,247)(232,246)(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)
(256,426)(257,442)(258,441)(259,440)(260,439)(261,438)(262,437)(263,436)
(264,435)(265,434)(266,433)(267,432)(268,431)(269,430)(270,429)(271,428)
(272,427)(273,409)(274,425)(275,424)(276,423)(277,422)(278,421)(279,420)
(280,419)(281,418)(282,417)(283,416)(284,415)(285,414)(286,413)(287,412)
(288,411)(289,410)(290,392)(291,408)(292,407)(293,406)(294,405)(295,404)
(296,403)(297,402)(298,401)(299,400)(300,399)(301,398)(302,397)(303,396)
(304,395)(305,394)(306,393)(307,375)(308,391)(309,390)(310,389)(311,388)
(312,387)(313,386)(314,385)(315,384)(316,383)(317,382)(318,381)(319,380)
(320,379)(321,378)(322,377)(323,376)(324,358)(325,374)(326,373)(327,372)
(328,371)(329,370)(330,369)(331,368)(332,367)(333,366)(334,365)(335,364)
(336,363)(337,362)(338,361)(339,360)(340,359)(342,357)(343,356)(344,355)
(345,354)(346,353)(347,352)(348,351)(349,350);
s2 := Sym(442)!( 1,223)( 2,222)( 3,238)( 4,237)( 5,236)( 6,235)( 7,234)
( 8,233)( 9,232)( 10,231)( 11,230)( 12,229)( 13,228)( 14,227)( 15,226)
( 16,225)( 17,224)( 18,240)( 19,239)( 20,255)( 21,254)( 22,253)( 23,252)
( 24,251)( 25,250)( 26,249)( 27,248)( 28,247)( 29,246)( 30,245)( 31,244)
( 32,243)( 33,242)( 34,241)( 35,257)( 36,256)( 37,272)( 38,271)( 39,270)
( 40,269)( 41,268)( 42,267)( 43,266)( 44,265)( 45,264)( 46,263)( 47,262)
( 48,261)( 49,260)( 50,259)( 51,258)( 52,274)( 53,273)( 54,289)( 55,288)
( 56,287)( 57,286)( 58,285)( 59,284)( 60,283)( 61,282)( 62,281)( 63,280)
( 64,279)( 65,278)( 66,277)( 67,276)( 68,275)( 69,291)( 70,290)( 71,306)
( 72,305)( 73,304)( 74,303)( 75,302)( 76,301)( 77,300)( 78,299)( 79,298)
( 80,297)( 81,296)( 82,295)( 83,294)( 84,293)( 85,292)( 86,308)( 87,307)
( 88,323)( 89,322)( 90,321)( 91,320)( 92,319)( 93,318)( 94,317)( 95,316)
( 96,315)( 97,314)( 98,313)( 99,312)(100,311)(101,310)(102,309)(103,325)
(104,324)(105,340)(106,339)(107,338)(108,337)(109,336)(110,335)(111,334)
(112,333)(113,332)(114,331)(115,330)(116,329)(117,328)(118,327)(119,326)
(120,342)(121,341)(122,357)(123,356)(124,355)(125,354)(126,353)(127,352)
(128,351)(129,350)(130,349)(131,348)(132,347)(133,346)(134,345)(135,344)
(136,343)(137,359)(138,358)(139,374)(140,373)(141,372)(142,371)(143,370)
(144,369)(145,368)(146,367)(147,366)(148,365)(149,364)(150,363)(151,362)
(152,361)(153,360)(154,376)(155,375)(156,391)(157,390)(158,389)(159,388)
(160,387)(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)
(168,379)(169,378)(170,377)(171,393)(172,392)(173,408)(174,407)(175,406)
(176,405)(177,404)(178,403)(179,402)(180,401)(181,400)(182,399)(183,398)
(184,397)(185,396)(186,395)(187,394)(188,410)(189,409)(190,425)(191,424)
(192,423)(193,422)(194,421)(195,420)(196,419)(197,418)(198,417)(199,416)
(200,415)(201,414)(202,413)(203,412)(204,411)(205,427)(206,426)(207,442)
(208,441)(209,440)(210,439)(211,438)(212,437)(213,436)(214,435)(215,434)
(216,433)(217,432)(218,431)(219,430)(220,429)(221,428);
poly := sub<Sym(442)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope